The DOI matches its Crossref record; 30 of the 30 references it cites were found in a registry or an index.
A geometric analysis of subspace clustering with outliers
Open accessAbstract
This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance how many subspaces there are nor do we have any information about their dimensions. We develop a novel geometric analysis of an algorithm named sparse subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern Recognition, 2009. CVPR 2009 (2009) 2790–2797. IEEE], which significantly broadens the range of problems where it is provably effective. For instance, we show that SSC can recover multiple subspaces, each of dimension comparable to the ambient dimension. We also prove that SSC can correctly cluster data points even when the subspaces of interest intersect. Further, we develop an extension of SSC that succeeds when the data set is corrupted with possibly overwhelmingly many outliers. Underlying our analysis are clear geometric insights, which may bear on other sparse recovery problems. A numerical study complements our theoretical analysis and demonstrates the effectiveness of these methods.
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Cites
Candes, E. J., Romberg, J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.862083 · Cited by 15,639
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Shi, J., & Malik, J. (2000) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.868688 · Cited by 15,502
On Spectral Clustering: Analysis and an algorithm
Ng, A. Y., Jordan, M. I., & Weiss, Y. (2001) · Cited by 8,159
Mixtures of Probabilistic Principal Component Analyzers
Tipping, M. E., & Bishop, C. M. (1999) · Neural Computation · doi:10.1162/089976699300016728 · Cited by 1,873
Robust Subspace Segmentation by Low-Rank Representation
Liu, G., Lin, Z., & Yu, Y. H. (2010) · Cited by 1,534
Elhamifar, E., & Vidal, R. (2009) · 2009 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2009.5206547 · Cited by 1,243
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Kriegel, H.-P., Kröger, P., & Zimek, A. (2009) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/1497577.1497578 · Cited by 1,093
Generalized principal component analysis (GPCA)
Vidal, R., Ma, Y., & Sastry, S. (2005) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2005.244 · Cited by 1,038
Asymptotic Theory of Finite Dimensional Normed Spaces
(1986) · Lecture Notes in Mathematics · doi:10.1007/bfb0075912 · Cited by 778
Cited by
Sparse Subspace Clustering: Algorithm, Theory, and Applications
Elhamifar, E., & Vidal, R. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2013.57 · Cited by 3,106
A holistic review of Network Anomaly Detection Systems: A comprehensive survey
Moustafa, N., Hu, J., & Slay, J. (2019) · Journal of Network and Computer Applications · doi:10.1016/j.jnca.2018.12.006 · Cited by 317
Generative Probabilistic Novelty Detection with Adversarial Autoencoders
Pidhorskyi, S., Almohsen, R., Adjeroh, D. A., & Doretto, G. (2018) · arXiv · doi:10.48550/arxiv.1807.02588 · Cited by 255
Metadata
- Authors
- Soltanolkotabi, M., & Candés, E. J.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2012-08-01
- Volume
- 40
- Issue
- 4
- Pages
- 2195-2238
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2139054653
- Cited by
- 411
- References
- 30
- FWCI
- 37.68
- Type
- journal article
- Language
- en
- Open access
- green
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